Interferometric speckle visibility spectroscopy

ABSTRACT

Interferometric speckle visibility spectroscopy methods, systems, and non-transitory computer readable media for recovering sample speckle field data or a speckle field pattern from an off-axis interferogram recorded by one or more sensors over an exposure time and determining sample dynamics of a sample being analyzed from speckle statistics of the speckle field data or the speckle field pattern.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/946,063, titled “INTERFEROMETRIC SPECKLE VISIBILITY SPECTROSCOPY” andfiled on Jun. 4, 2020, which claims priority to and benefit of U.S.Provisional Patent Application No. 62/856,963, titled “InterferometricSpeckle Visibility Spectroscopy” and filed on Jun. 4, 2019; both ofwhich are hereby incorporated by reference in their entirety and for allpurposes.

FIELD

Certain embodiments pertain to interferometric speckle visibilityspectroscopy systems and methods that can be implemented in, forexample, biomedical measurements and atmospheric measurements.

BACKGROUND

High-fidelity measurement of functional and structural informationinside biological tissue is critical in many fields of biomedicine.Light offers advantages in biological imaging since it can be safelyused, can measure biological information at the cellular scale, and cansupport high temporal resolutions. However, light-based imaging methodshave been stymied by the optical opacity of biological tissue due to itsrefractive index heterogeneity, which can prevent imaging deeply withinthe tissue. Methods such as optical wavefront shaping have been able toreclaim scattered light and peer deeper into tissue for high-resolutionimaging and excitation, but these methods require complicated opticalsetups.

SUMMARY

Certain aspects pertain to methods for interferometric specklevisibility spectroscopy. These methods include (i) recovering samplespeckle field data or a speckle field pattern from an off-axisinterferogram recorded by one or more sensors over an exposure time; and(ii) determining sample dynamics of a sample being analyzed from specklestatistics of the speckle field data or the speckle field pattern. Inone implementation, the sample dynamics comprise a decorrelation timeand/or a movement of an object in the sample. In some cases, the samplespeckle field data is recovered by Fourier transforming the off-axisinterferogram to generate data in spatial frequency space comprising atleast one off-axis lobe and using a spatial frequency filter to crop thesample speckle field data from the at least one off-axis lobe.

Certain aspects pertain to non-transitory computer readable media forinterferometric speckle visibility spectroscopy. The non-transitorycomputer readable media comprises program instructions, wherein theprogram instructions, when executed by one or more processors, areconfigured to cause the one or more processors to (i) recover samplespeckle field data or a speckle field pattern from an off-axisinterferogram recorded by one or more sensors over an exposure time and(ii) determine sample dynamics of a sample being analyzed from specklestatistics of the speckle field data or the speckle field pattern. Inone implementation, the sample dynamics comprise a decorrelation timeand/or a movement of an object in the sample. In some cases, the samplespeckle field data is recovered by Fourier transforming the off-axisinterferogram to generate data in spatial frequency space comprising atleast one off-axis lobe and using a spatial frequency filter to crop thesample speckle field data from the at least one off-axis lobe.

Certain aspects pertain to interferometric speckle visibilityspectroscopy systems. These systems includes one or more optical systemsconfigured to interfere an off-axis reference beam with a sample signalat one or more sensors and one or more processors configured to executeinstructions to cause the one or more processors to (i) recover samplespeckle field data or a speckle field pattern from an off-axisinterferogram recorded by one or more sensors over an exposure time and(ii) determine sample dynamics of a sample being analyzed from specklestatistics of the speckle field data or the speckle field pattern.

These and other features are described in more detail below withreference to the associated drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A depicts five (5) speckle patterns measured by an interferometricspeckle visibility spectroscopy (iSVS) system at times t₁-t₅ where thescattering medium is static, according to embodiments.

FIG. 1B depicts five (5) speckle patterns measured by an interferometricspeckle visibility spectroscopy (iSVS) system at times t₁-t₅ where thescattering medium is decorrelating, according to embodiments.

FIG. 2 is a schematic diagram illustrating an example of a sequence ofoperations of an iSVS method for recovering a sample speckle fieldpattern from an off-axis interferogram recorded during a single exposuretime, according to one embodiment.

FIG. 3 is a flowchart depicting operations of an iSVS method, accordingto implementations.

FIG. 4 is a flowchart depicting sub-operations of an operation of aniSVS method, according to an implementation.

FIG. 5 is a flowchart depicting sub-operations of an operation of aniSVS method, according to an implementation.

FIG. 6 is a flowchart depicting operations of an iSVS method forcalibrating an iSVS system, according to an implementation.

FIG. 7 is a simplified block diagram of components of an iSVS system,according to implementations.

FIG. 8A is a schematic diagram of components of an iSVS system 800 inreflection mode, according to one implementation.

FIG. 8B is a schematic diagram of components of an iSVS system 900 intransmission mode, according to certain implementations

FIG. 9A is an illustration of an example of an off-axis holographyspatial frequency spectrum with a circular sample bandwidth implementedby using a circular aperture at the Fourier plane of an iSVS system,according to an implementation,

FIG. 9B is an illustration of an example of an off-axis holographyspatial frequency spectrum with a rectangular sample bandwidthimplemented by using a rectangular aperture at the Fourier plane of aniSVS system, according to an implementation

FIG. 10A is a photograph of an examples of components of a calibrationsubsystem of an iSVS system including a rotating diffuser and a motorand gearbox, according to one aspect.

FIG. 10B is a schematic diagram of an example of components of acalibration subsystem of an iSVS system, according to one aspect.

FIG. 11 is a graph with a plot of decorrelation times measured by acalibration subsystem for different motor speeds controlled by controlsignals from a motor controller in communication with the motor,according to one aspect.

FIG. 12A is a graph of a plot of speckle contrast determined by an SVSsystem vs. decorrelation time, according an aspect.

FIG. 12B is a graph with a plot of effective visibility factordetermined by an iSVS system vs. decorrelation time as measured by acalibration subsystem, according an aspect.

FIGS. 13A, 14A, 15A, 16A, 17A, and 18A are graphs with plots ofeffective speckle visibility over time (seconds) for the dorsal skinflap as measured by the iSVS system in transmission mode (e.g., iSVSsystem 900 shown in FIG. 8B) where the laser powers were 1 mW, 0.5 mW,0.26 mW, 0.13 mW, 0.06 mW, and 0.03 mW respectively, according toimplementations.

FIG. 13A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system intransmission mode where the laser power was 1 mW, according to oneexample.

FIG. 13B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system intransmission mode where the laser power was 1 mW, according to oneexample.

FIG. 14A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system intransmission mode where the laser power was 0.5 mW, according to oneexample.

FIG. 14B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system intransmission mode where the laser power was 0.5 mW, according to oneexample.

FIG. 15A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system intransmission mode where the laser power was 0.26 mW, according to oneexample.

FIG. 15B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system intransmission mode where the laser power was 0.26 mW, according to oneexample.

FIG. 16A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system intransmission mode where the laser power was 0.13 mW, according to oneexample.

FIG. 16B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system intransmission mode where the laser power was 0.13 mW, according to oneexample.

FIG. 17A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system intransmission mode where the laser power was 0.06 mW, according to oneexample.

FIG. 17B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system intransmission mode where the laser power was 0.06 mW, according to oneexample.

FIG. 18A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system intransmission mode where the laser power was 0.03 mW, according to oneexample.

FIG. 18B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system intransmission mode where the laser power was 0.03 mW, according to oneexample.

FIG. 19A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system inreflection mode where the laser power was 1.0 mW, according to oneexample.

FIG. 19B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system inreflection mode where the laser power was 1.0 mW, according to oneexample.

FIG. 20A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system inreflection mode where the laser power was 0.50 mW, according to oneexample.

FIG. 20B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system inreflection mode where the laser power was 1.0 mW, according to oneexample.

FIG. 21A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system inreflection mode where the laser power was 0.26 mW, according to oneexample.

FIG. 21B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system inreflection mode where the laser power was 0.26 mW, according to oneexample.

FIG. 22A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system inreflection mode where the laser power was 0.13 mW, according to oneexample.

FIG. 22B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system inreflection mode where the laser power was 0.13 mW, according to oneexample.

FIG. 23A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system inreflection mode where the laser power was 0.06 mW, according to oneexample.

FIG. 23B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system inreflection mode where the laser power was 0.06 mW, according to oneexample.

FIG. 24A is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an iSVS system inreflection mode where the laser power was 0.03 mW, according to oneexample.

FIG. 24B is a graph with a plot of effective speckle visibility overtime (seconds) for a dorsal skin flap as measured by an SVS system inreflection mode where the laser power was 0.03 mW, according to oneexample.

FIG. 25 is a schematic diagram of components of an iSVS system,according to an embodiment.

FIG. 26 is a graph of a plot of the intensity decorrelation curve g2(t)measured by the iSVS system shown in FIG. 25 , according to an example.

FIG. 27 is a graph of a plot of the visibility factors measured at 100Hz on the forehead of a human subject using the iSVS system shown inFIG. 25 , according to an example.

FIG. 28 is a graph of a plot of the blood flow index calculated from thevisibility factors in FIG. 27 , according to an example.

FIG. 29 is a graph of a plot of the Fourier transform of the curve shownin FIG. 28 , according to an example.

FIG. 30 is a graph of a plot of the heart beat frequency measured by aniSVS system, according to an example.

FIG. 31 is a graph of a plot of cerebral blood flow traces measured byan iSVS system when the human subject was holding breath, according toan example.

FIG. 32 is a graph of statistical analysis results of cerebral bloodflow changes at different phases, according to an example.

DETAILED DESCRIPTION

Different aspects are described below with reference to the accompanyingdrawings. The features illustrated in the drawings may not be to scale.In the following description, numerous specific details are set forth inorder to provide a thorough understanding of the presented embodiments.The disclosed embodiments may be practiced without one or more of thesespecific details. In other instances, well-known operations have notbeen described in detail to avoid unnecessarily obscuring the disclosedembodiments. While the disclosed embodiments will be described inconjunction with the specific embodiments, it will be understood that itis not intended to limit the disclosed embodiments. Moreover, althoughmany disclosed embodiments of interferometric speckle visibilityspectroscopy (iSVS) methods and systems will be described for biomedicalapplications such as used in determining the dynamics of blood flow, itwould be understood that these embodiments are not so limited. The iSVSmethods and systems disclosed herein can also have applications in otherareas such as, for example, determining dynamics of atmosphericmeasurements.

I. Introduction

-   -   Sample Dynamics

When coherent light illuminates a dynamic scattering sample such asliving tissue, the interference of the different scattered lightcomponents generates an optical interference pattern called a specklefield. When the scatterers within the sample move, this generatestemporal fluctuations in the speckle pattern. These changes in thespeckle pattern are related to the movement of scatterers (i.e.,scattering objects) within the sample.

Generally speaking, there are two main techniques to calculate themovement speed of an object and other sample dynamics. Here sampledynamics refers to the movement of an element or elements within asample. For example, in the context of biological imaging, particlessuch as red blood cells may be circulating and impart changes to theoptical transmission of light through the sample over time. Other typesof sample dynamics may include, for example, the movement of a vehicleor person within an optically scattering medium such as a fog or cloud.One technique is to use a high-speed sensor (such as a single pixeldetector like a single photon counting module or avalanche photodetectoror a high-speed array detector such as a CMOS or 2D single photonavalanche diode) to capture multiple measurements and directly calculatethe correlation between subsequent frames at times t_(i) to calculatemovement speed of the scattering object. This technique generallyrequires a high-speed device with a frame rate capable of capturingmultiple frames within a single decorrelation time. An example of thisfirst technique is diffusing wave spectroscopy (DWS), which is discussedin Pine, D., Weitz, D., Zhu, J., and Herbolzheimer, E., “Diffusing-wavespectroscopy: Dynamic light scattering in the multiple scatteringlimit,” Journal de Physique, vol. 51, no. 18, pp. 2101-2127,1990, whichis hereby incorporated by reference in its entirety. The application ofthe DWS technique to biological tissue, e.g., to measure blood flowspeed, is diffuse correlation spectroscopy (DCS), which is discussed inBoas, D. A., Campbell, L., and Yodh, A. G., “Scattering and imaging withdiffusing temporal field correlations,” Physical Review Letters, vol.75, no. 9, pp. 1855-1858 (1995), which is hereby incorporated byreference in its entirety. Examples of DCS systems can be found inCheung, C., Culver, J. P., Takahashi, K., Greenberg, J. H., Yodh, A. G.,“In vivo cerebrovascular measurement combining diffuse near-infraredabsorption and correlation spectroscopies,” Phys. Med. Biol.46,2053-2065 (2001) and Huppert, T. J., Diamond, S. G., Franceschini, M.A., Boas, D. A., “HomER: A review of time-series analysis methods fornear-infrared spectroscopy of the brain,”Appl. Opt. 48 (2009), which arehereby incorporated by reference in their entireties. In one example ofa DCS system, a sensitive single-pixel photodetector, such as anavalanche photodiode, is used to collect light from a single specklegrain of the speckle pattern and monitor its fluctuations over time.Then, by computing the temporal autocorrelation function of theintensity time trace, g₂(t), the decay can be fit to a theoretical modelto extract quantities of interest such as the diffusion coefficient ofthe sample under test. One of the limitations of this DCS system is thatit can only sample light from a single speckle grain or a few specklegrains in order to maximize contrast and signal-to-noise ratio (SNR) inthe measurement, which fundamentally limits throughput of themeasurement. The performance of this DCS system is ultimatelyconstrained by the total collected photon budget required for areasonable SNR. Since this DCS system exploits only one or a fewspeckles grains from the scattered light, in order to get a sufficientnumber of signal photons for a relatively accurate measure of the sampleflow dynamics, the required measurement time of the detector for onedata point (e.g. one measurement of cerebral blood flow (CBF)) istypically no less than tens of milliseconds. There is therefore atradeoff between the measurement time and the sensitivity of the system:a high SNR measurement requires a relatively long measurement time,which results in a relatively low sampling rate.

Another technique for calculating the movement speed of a scatteringobject is to infer the speed from the blurring of the object within animage frame recorded during a single exposure time, T. The amount ofblurring can be used to quantitatively determine how fast the sample isdecorrelating (i.e., the decorrelation time). By using the blurringinference based on a single exposure time to measure decorrelation timeinstead of direct calculation from multiple frames, it is no longernecessary to capture multiple frames within a single decorrelation time,which relaxes requirement for a high frame rate. As used herein, a“decorrelation time” refers to the point when the temporalautocorrelation function g₁(t) drops below a certain threshold.Depending on the specific form of g₁(t), some common choices for thisthreshold are 1/e or 1/e². The decorrelation time is calculated bycomputing the temporal autocorrelation function using the measured dataand then extracting the point at which the function drops below thethreshold from a theoretical model fitted to the data. The movementspeed can also be determined from the parameters of the fitted modelwhich take into account the impact of the sample dynamics on theautocorrelation function.

An example of a technique that uses the blurring inference to be able tocalculate decorrelation time is speckle visibility spectroscopy (SVS).Conventional SVS measures the decorrelation time from a single frameusing statistics of the blurred speckle patterns captured during asingle exposure time longer than the decorrelation time. One example ofa conventional SVS system uses a camera with a detector array, such as acharge-coupled device (CCD) camera, to capture a two-dimensional specklepattern containing many speckle grains, and uses the statisticsdetermined from the blurred speckle pattern to calculate the speckledecorrelation time. For a given camera integration (exposure) time thatis longer than the speckle decorrelation time, different speckledecorrelation times result in speckle pattern frames with differentextents of blurring. Examples of conventional SVS systems can be foundin Dunn, A. K., Bolay, H., Moskowitz, M. A., Boas, D. A., “Dynamicimaging of cerebral blood flow using laser speckle,” J. Cereb. BloodFlow Metab. 21, 195-201 (2001), Bandyopadhyay, R., Gittings, A. S. Suh,S. S. Dixon, P. K., Durian, D. J., “Speckle-visibility spectroscopy: Atool to study time-varying dynamics,” Rev. Sci. Instrum. 76 (2005),Dunn, A. K., “Laser speckle contrast imaging of cerebral blood flow,”Ann. Biomed. Eng. 40, 367-377 (2012), Valdes, C. P., Varma, H. M.,Kristoffersen, A. K., Dragojevic, T., Culver, J. P., Durduran, T.,“Speckle contrast optical spectroscopy, a non-invasive, diffuse opticalmethod for measuring microvascular blood flow in tissue,” Biomed. Opt.Express. 5, 2769 (2014), and Zhao, M., Mazdeyasna, S., Huang, C.,Agochukwu-Nwubah, N., Bonaroti, A., Wong, L., Yu, G., “NoncontactSpeckle Contrast Diffuse Correlation Tomography of Blood FlowDistributions in Burn Wounds: A Preliminary Study,” Military Medicine,vol. 185, pp. 82-87 (2020), which are hereby incorporated by referencein their entireties.

Conventional SVS systems use a camera to record the intensitydistribution of dynamic speckle fields which are then used tocharacterize the speckle field decorrelation time τ. If the cameraexposure time T is longer than the speckle field decorrelation time τ,there will be multiple independent speckle fields recorded by the camerawithin the exposure time. Since these independent speckle fields arriveat the camera at different times, the speckle pattern recorded over theentire exposure is the intensity summation of these independent specklepatterns. If the speckle pattern does not decorrelate (e.g., when thesample is static), then the intensity summation over the exposure timesimply records a scaled version of a stable speckle pattern. However, ifthe speckle changes during the exposure time, the independent specklepatterns will add incoherently and ultimately modify the statistics ofthe recorded speckle pattern.

One statistic of interest in a speckle pattern is speckle contrast (κ),defined as:

$\begin{matrix}{{\kappa = \frac{\sigma}{\mu}},} & \left( {{Eqn}.1} \right)\end{matrix}$where σ is the standard deviation of the recorded speckle pattern and μis the mean intensity of the recorded speckle pattern.

Speckle contrast decreases as multiple independent speckle intensitypatterns add up on the camera, and mathematical models have beendeveloped which relate the measured speckle pattern contrast to thecamera exposure time T and the speckle field decorrelation time r asdiscussed in Boas, D. A. and Dunn, A. K., “Laser speckle contrastimaging in biomedical optics,” Journal of Biomedical Optics, vol. 15,no. 1, p. 011 109 (2010), which is hereby incorporated by reference inits entirety. Exploiting this relationship, the speckle fielddecorrelation time can be calculated by measuring the speckle patterncontrast and inferring information about the activities that influencedthe dynamic properties of the scattering sample.

There are, however, two conditions that must be satisfied when usingconventional SVS to take measurements that can be used to accuratelycalculate dynamic properties: (1) the Siegert relation should hold(“Condition 1”), and (2) the photon number should be large enough tooverwhelm the camera noise (“Condition 2”). For Condition 1, the Siegertrelation assumes a fully-developed speckle pattern and then takesadvantage of its statistical properties to convert the intensityautocorrelation function g₂(t) to the complex field autocorrelationfunction g₁(t). If the speckles are not fully developed, which canhappen if the photons do not experience multiple scattering events inthe scattering medium, the output speckle pattern no longer followsfully-developed speckle statistics as discussed in “Some fundamentalproperties of speckle,” JOSA, vol. 66, no. 11, pp. 1145-1150 (1976),which is hereby incorporated by reference in its entirety. In this case,the Siegert relation does not hold and there is no direct connectionbetween g₂(t) and g₁(t). Moreover, there is an empirical factor β whenconverting g₂(t) to g₁(t), which also introduces systematic inaccuracyto the measurement. For Condition 2, if the speckle field decorrelationtime changes quickly, the camera should have a short exposure time andhigh frame rate to monitor the change of the decorrelation time, whichlimits the number of available signal photons in each frame. In thiscase, the dark current and readout noise of the camera can swamp thesample signal. Thus, conventional SVS takes measurements that sufferfrom camera noise, which limits the sensitivity of SVS techniques.Moreover, when using conventional SVS to detect photons delivered intosamples at depths, e.g., greater than 1 cm, the amount of reflectedphotons reaching the detector array may be less than 1 photon/pixelwithin an exposure time. In these cases, camera noise may overwhelm theweak signal from detected deep photons.

II. Interferometric Speckle Visibility Spectroscopy (iSVS)

Certain aspects pertaining to interferometric speckle visibilityspectroscopy (iSVS) systems and methods circumvent the two conditionsdiscussed in Section I above, and thus, can determine g₁(t) directlywithout needing to use g₂(t) and β. These iSVS systems and/or methodsimplement an interferometric optical arrangement (e.g., off-axisholography) to boost the sample signal to overcome camera noise. Forexample, an iSVS system and/or method of one implementation can boostthe signal to achieve a suitable signal-to-noise ratio (SNR) when themean pixel value from the sample signal is less than 1. In one aspect,iSVS systems and/or methods described herein use interferometricmeasurements of the electrical field magnitude of a single frame (i.e.,interferogram) recorded during a single exposure time to calculate adecorrelation time of the sample. The iSVS systems and/or methods infersample dynamics from the speckle statistics measured in a single framespeckle pattern recorded. Certain iSVS systems and/or methods describedherein enable high-speed and sensitive measurement of the optical fielddynamics with shot-noise limited sensitivity.

When a scattering medium is static, the electric field remains constantthrough all the time stamps during a single decorrelation time. Thisresults in an overall integrated electric field which is a scaledversion of the static speckle pattern. However, when the sample isdecorrelating, the electric field changes as a function of time. Thisgenerates a speckle pattern with a lower average amplitude, since theresultant electric field phasor at each point within the frame is anaverage of a series of phasors with random amplitudes and phases.Therefore, the average value of the speckle electric field can be usedto quantitatively measure the decorrelation time of the sample.

In certain implementations, the exposure time of the one or more sensorsof the camera is set to at least one order of magnitude longer than thedecorrelation time. In one example, the exposure time of the one or moresensors of the camera is set as one order of magnitude longer than thedecorrelation time, i.e., 10 times longer.

The decorrelation time used to calculate the exposure time can beestimated from D. Wang, A. B. Parthasarathy, W. B. Baker, K. Gannon, V.Kavuri, T. Ko, S. Schenkel, Z. Li, Z. Li, M. T. Mullen, J. A. Detre, A.G. Yodh, Fast blood flow monitoring in deep tissues with real-timesoftware correlators. Biomed. Opt. Express. 7, 776 (2016), which ishereby incorporated by reference in its entirety. Alternatively, thedecorrelation time used to determine the exposure time can be determinedusing a conventional DCS method. Once the decorrelation time isestimated, the exposure time can be set accordingly and more accuratemeasurements can be taken by the iSVS system.

According to certain aspects, iSVS systems include an off-axisinterferometric optical arrangement that implements a tilted referencebeam (e.g., a plane wave reference beam tilted an oblique angle θ) tointerfere with the sample signal at the one or more sensors of thecamera, and the camera records one or more off-axis holograms (alsoreferred to herein as “off-axis interferograms”). Each off-axis hologramrecorded by the camera is a measurement of the intensity of theinterference pattern integrated over a single exposure time. Therecorded data from an off-axis hologram can be used in single-shotcomplex sample field reconstruction. The off-axis interferometricarrangement removes the constraint of condition 1 since the complexsample field can be retrieved from the off-axis holograms and the g₁(t)can be calculated directly. Also, the reference beam enables the lowsignal field to be boosted above the camera noise threshold using theheterodyne gain of the reference beam, and thus, the constraints ofcondition 2 become less restrictive or no longer restrictive.

According to certain aspects, an iSVS system and/or method implements atilted planar reference beam for off-axis hologram acquisition. In theseaspects, the tilted planar reference beam, E_(r)(r, t)=E₀(r)exp(ik·r),and the sample beam, E_(s)(r, t)=E_(s)(r)exp(iϕ_(s)(r, t)), interfere onthe camera, where r=(x, y) is the spatial coordinate, t is the time, E₀is the amplitude of the reference beam, k is the wave vectorcorresponding to the tilted plane wave reference beam, and E_(s)(r, t)and ϕ_(s)(r, t) are the amplitude and phase of the signal light field,respectively. The camera can record over an exposure time an intensityspeckle pattern I(r) at position r=(x, y) due to the interference of thesample and the reference beam given by:I(r)=∫₀ ^(T) |E _(r)(r, t)+E _(S)(r, t)|² dt=∫ ₀ ^(T) |E _(r)(r, t)|²+|E _(S)(r, t)|²+2E _(r)(r, t)E _(S)(r, t)cos(k·r−ϕ _(S)(r, t)dt   (Eqn.2)where t=0 defines the beginning of the exposure and T is the exposuretime. Since the reference beam is tilted at a tilt angle θ with respectto the sample beam for off-axis holography, this generates aninterference fringe pattern that separates the third term in Eqn. 2 inthe spatial frequency domain from the other data. Therefore, by takingthe Fourier transform of the captured off-axis hologram I(r) in Eqn. 2,and using the known planar reference beam field profile, the complexsample field can be recovered by spatially filtering the image in thespatial frequency domain as discussed below.

In certain implementations, the iSVS systems and/or methods areconfigured to take the Fourier transform of an off-axis interferogramwhich results in data having three distinct lobes as described belowwith reference to an example shown in FIG. 2 . The data from the centrallobe corresponds to the Fourier transform of the combined first twoterms (DC terms) in Eqn. 2. The data from the two side lobes correspondsto the Fourier transform of the third term in Eqn. 2. According tocertain implementations, iSVS systems and/or methods isolate the datafrom at least one of the two side lobes in the spatial frequency domainto extract the complex sample field E_(S)( r, t). Since these two lobescontain the same information and are simply complex conjugates of eachother (commonly referred to as twin images in off-axis holography),either lobe may be used to extract the sample dynamics. After extractingthe complex sample field E_(S)( r, t) from the off-axis interferogram,speckle statistics of this sample speckle field can be further analyzedto retrieve the dynamics of the scattering sample (sample dynamics). Itshould be noted that the two side lobes in Fourier plane are phaseconjugate pairs, therefore extracting one of the pairs is sufficient forreconstructing the sample field. The sample dynamics are directly linkedto the average amplitude of the sample speckle field. If the sample isstatic, then the overall amplitude of the sample speckle field is at itsmaximum. If the sample is decorrelating, the overall average amplitudeof the sample speckle field decreases. The degree to which it decreasesprovides a quantitative measure of the decorrelation time.

FIGS. 1A and 1B is an illustration for the purpose of depicting thedifference between the static and decorrelating samples in iSVSmeasurements (e.g., intensity measurements) recorded over an exposuretime that are integrated to generate a recorded hologram. FIG. 1Aincludes five (5) iSVS measurements of the sample speckle field take attimes t₁-t₅ during an exposure time where the scattering medium isstatic. At each time t₁-t₅, the sample speckle field is the same duringthe iSVS measurements in FIG. 1A. FIG. 1B includes five (5) iSVSmeasurements of the sample speckle field take at times t₁-t₅ where thescattering medium is decorrelating. In this example, the scatteringmedium is decorrelating and the measurements of the sample specklepattern at the time stamps t₁-t₅ taken over the exposure time aredifferent.

As illustrated in FIG. 1A, if the sample speckle field is static, thenthe amplitude and phase of a specific coherence area (i.e., a specklegrain) is fixed as a function of time. Thus, the integration of thestatic sample field over the exposure time in the recorded hologram willsimply create a scaled version of the measured static speckle pattern.

On the other hand, if the sample speckle field is decorrelating due tomotion within the scattering medium as illustrated in FIG. 1B, thecomplex amplitude and phase of the sample speckle field will fluctuateas a function of time. The effect of this fluctuation will be to createa new sample speckle pattern measurement that will have a lower averagemagnitude than the static case, since the integrated sample electricfield will effectively result in the summation of a random walk in thecomplex plane at each speckle grain where the amplitude and phase of thephasor is drawn from the corresponding statistical distributions knownfor speckle (e.g., Rayleigh distributed amplitude and uniformlydistributed phase).

Defining the heterodyne signal as:

$\begin{matrix}{{S(r)} = {\frac{1}{T}{\int_{0}^{T}{2{E_{0}(r)}{E_{s}\left( {r,t} \right)}{\cos\left( {{k \cdot r} - {\phi_{s}\left( {r,t} \right)}} \right)}{dt}}}}} & \left( {{Eqn}.3} \right)\end{matrix}$

The second moment of S(r) contains the field decorrelation functiong₁(t):

$\begin{matrix}\begin{matrix}{\left\langle {S(r)}^{2} \right\rangle = {\frac{4E_{0}^{2}}{T^{2}}\left\langle {\int_{0}^{T}{\int_{0}^{T}{{E_{s}\left( {r,t_{1}} \right)}{\cos\left( {{k \cdot r} - {\phi_{s}\left( {r,t_{1}} \right)}} \right)}{E_{s}\left( {r,t_{1}} \right)}}}} \right.}} \\\left. {}{{\cos\left( {{k \cdot r} - {\phi_{s}\left( {r,t_{1}} \right)}} \right)}{dt}_{1}{dt}_{1}} \right\rangle \\{= {\frac{4E_{0}^{2}\overset{\_}{E_{s}^{2}}}{T}{\int_{0}^{T}{2\left( {1 - \frac{t}{T}} \right)\left( {g_{1}(t)} \right)^{2}{dt}}}}} \\{= {\frac{4I_{0}^{2}\overset{\_}{I_{s}^{2}}}{T}{\int_{0}^{T}{2\left( {1 - \frac{t}{T}} \right)\left( {g_{1}(t)} \right)^{2}{dt}}}}}\end{matrix} & \left( {{Eqn}.4} \right)\end{matrix}$

As shown in Eqn. 4, the second moment of S(r) is a function of theintegrated value of g₁(t) over the exposure time, weighted by a factorinversely proportional to the exposure time T. In the case where oursample field is a speckle pattern, the second moment is a measure of theblurring of the speckle pattern. If the sample is slowly decorrelatingover the exposure time (i.e., g₁(t)≈1 for 0<t<T), then the result of theintegral is:

$\begin{matrix}\begin{matrix}{\left\langle {S(r)}^{2} \right\rangle = {\frac{4I_{0}\overset{\_}{I_{s}}}{T}{\int_{0}^{T}{2\left( {1 - \frac{t}{T}} \right)\left( {g_{1}(t)} \right)^{2}{dt}}}}} \\{= {\frac{4I_{0}\overset{\_}{I_{s}}}{T} \cdot T}} \\{= {4I_{0}\overset{\_}{I_{s}}}}\end{matrix} & \left( {{Eqn}.5} \right)\end{matrix}$

As the decorrelation time increases and the value of g₁(t) begins tosignificantly decay from 1 during the exposure time T, the value of

S(r)²

will decrease. In the limit where the value of g₁(t) decays quickly to 0relative to the exposure time, the value of

S(r)²

decays to zero. Therefore, by measuring the second moment of the samplespeckle field, the decorrelation time can be inferred.

Another Example

Another way to express the total instantaneous interference patternI_(t)(r) at the position r=(x, y) in the observation plane is:I _(t)(r)=|E _(r)|² +|E _(S)(r)|²+2|E _(r) ∥E _(S)(r)|cos(k ₀×sinθx+ϕ_(S)(r))=I _(R) +I _(S)(r)+2√{square root over (I _(R) I _(S)(r))}cos(k₀ xsinθ+ϕ_(S)(r)  (Eqn. 6)where E_(R) is the complex light field of the plane wave reference beam,E_(S)(r) is the complex light field of the sample beam, ϕ_(s)(r) is thephase difference between the reference beam and the sample beam, k₀ isthe wave vector corresponding to the tilted plane wave reference beam,and θ is the oblique tilt angle of the reference beam.

The interference pattern recorded by the camera is:I(r)=∫₀ ^(T)(|E _(r)|² +|E _(S)(r, t)|²+2|E _(r) ∥E _(S) 9 r, t)|cos(k ₀xcosθx+ϕ _(S)(r, t) dt   (Eqn. 7)

The interference signal H(r) is defined as:

$\begin{matrix}\begin{matrix}{{H(r)} = {\frac{1}{T}{\int_{0}^{T}{\left( {2{❘{E_{r}│\, │\,{E_{s}\left( {r,t} \right)}}❘}\cos{\phi_{s}\left( {r,t} \right)}} \right){dt}}}}} \\{= {\frac{1}{T}{\int_{0}^{T}\left( {{{❘{E_{r}│\, │\,{E_{s}\left( {r,t} \right)}}❘}{\exp\left( {i{\phi_{s}\left( {r,t} \right)}} \right)}{dt}} +} \right.}}} \\{\frac{1}{T}{\int_{0}^{T}\left( {{❘{E_{r}│\, │\,{E_{s}\left( {r,t} \right)}}❘}{\exp\left( {{- i}{\phi_{s}\left( {r,t} \right)}} \right)}{dt}} \right.}}\end{matrix} & \left( {{Eqn}.8} \right)\end{matrix}$

By selecting the first conjugate pair, the iSVS signal S(r) can bedefined as:

$\begin{matrix}{{S(r)} = {\frac{1}{T}{\int_{0}^{T}\left( {{❘{E_{r}│\, │\,{E_{s}\left( {r,t} \right)}}❘}{\exp\left( {i{\phi_{s}\left( {r,t} \right)}} \right)}{dt}} \right.}}} & \left( {{Eqn}.9} \right)\end{matrix}$

In one example, the field decorrelation can be defined as:

$\begin{matrix}{{g_{1}(t)} = \frac{\left\langle {{E_{s}\left( {r,t_{0}} \right)}{E_{s}^{*}\left( {r,{t_{0} + t}} \right)}} \right\rangle}{\left\langle {❘{E_{s}\left( {r,t_{0}} \right)}❘}^{2} \right\rangle_{t_{0}}}} & \left( {{Eqn}.10} \right)\end{matrix}$

The second moment of the iSVS signal S(r) contains the fielddecorrelation as:

$\begin{matrix}\begin{matrix}{\left\langle {S(r)}^{2} \right\rangle = {\frac{I_{R}}{T^{2}}\left\langle {\int_{0}^{T}{\int_{0}^{T}{{❘{E_{s}\left( {r,t_{1}} \right)}❘}{\exp\left( {i{\phi_{s}\left( {r,t_{1}} \right)}} \right)}{E_{s}\left( {r,t_{2}} \right)}}}} \right.}} \\\left. {}{\exp\left( {{- i}{\phi_{s}\left( {r,t_{2}} \right)}} \right)} \right\rangle \\{= {\frac{I_{R}\overset{\_}{I_{s}}}{T}{\int_{0}^{T}{2\left( {1 - \frac{t}{T}} \right){g_{1}(t)}{dt}}}}}\end{matrix} & \left( {{Eqn}.11} \right)\end{matrix}$where

·

_(t) _(O) denotes the expected value over to,

·

denotes the expected value space, I_(R) is the intensity of thereference beam, Ī_(S) is the mean intensity of the signal beam. Both ofI_(R)and Ī_(S) can be determined from a calibration operation such asthe calibration operation discussed in Section III.

An interference fringe visibility factor F is defined as:

$\begin{matrix}{F = {\frac{\left\langle {S(r)}^{2} \right\rangle}{I_{R}\overset{\_}{I_{s}}} = {\frac{1}{T}{\int_{0}^{T}{2\left( {1 - \frac{t}{T}} \right){g_{1}(t)}{dt}}}}}} & \left( {{Eqn}.12} \right)\end{matrix}$

The interference fringe visibility factor F ranges from 0 (minimumvisibility) to 1 (maximum visibility) depending on g₁(t). If the sampleis static (i.e., g₁(t)=1 or about 1 for 0<t<T), the interference fringevisibility factor F=1 or about 1 respectively. If the complex field ofthe sample light field is decorrelating, the interference fringevisibility factor F will be less than 1, e.g., in a range from aboutzero to about 1.0. If the complex field of the sample light field isdecorrelating quickly as compared to the exposure time T, for example,where g₁(t)=1 or nearly 1 for 0<t<τ and g₁(t)=0 or nearly 0 for τ<<Twhere τ<<t), then the visibility factor can be expressed as

$F = {\frac{2\tau}{T}.}$In this case, multiple decorrelation events within a single cameraexposure time may blur the inference fringes, yielding low fringevisibility.

-   -   Example Applications of iSVS Systems and/or Methods

1) Blood Flow Example

Scattered light can be directly analyzed to yield functional informationabout activity within tissue. For example, the measured dynamics ofcerebral blood flow (CBF) within brain tissue can be used as anindication of neuronal activity, providing non-invasive functionalinformation.

According to one aspect, interferometric speckle visibility spectroscopy(iSVS) methods and/or systems can perform interferometric measurementsthat enable sensitive, high-speed monitoring of blood flow dynamics. Thedynamics of blood flow within tissue are a key indicator of metabolicfunction, providing functional information about physiological activity.In certain implementations, iSVS methods and/or systems can be used tomeasure blood flow dynamics non-invasively using the dynamic propertiesof a captured optical field that has interacted with blood in a volumeof interest. Certain embodiments of iSVS systems and methods describedherein implement a large-pixel-count camera and/or implement a referencebeam to interfere with scattered light from the sample to enablehigh-sensitivity measurement of the decorrelation inside the sample suchas tissue, even at low light intensities.

2) Atmospheric Measurements Example

According to another aspect, interferometric speckle visibilityspectroscopy (iSVS) methods and systems can perform interferometricmeasurements that enable high-sensitivity measurement of thedecorrelation for evaluation of atmospheric dynamics. An example of atechnique that can be implemented to determine the atmospheric dynamicsfrom the correlation determined by an iSVS system and/or method can befound in Ancellet, Gerard M. and Menzies, Robert T., “Atmosphericcorrelation-time measurements and effects on coherent Doppler lidar,” J.Opt. Soc. Am. A 4, 367-373 (1987), which is hereby incorporated byreference in its entirety.

III. Interferometric Speckle Visibility Spectroscopy (iSVS) Methods

Certain aspects pertain to iSVS methods that include operations fordetermining sample dynamics from one or more off-axis interferograms.According to one aspect, an iSVS method includes (i) recovering samplespeckle field data from an off-axis interferogram recorded over a singleexposure time, and (ii) determining sample dynamics from specklestatistics of the sample speckle field data. The off-axis interferogramcaptured by the camera includes both sample speckle field data andreference beam data. The iSVS method performs Fourier transform on theoff-axis interferogram to reveal off-axis lobes that contain samplespeckle field data and a third central lobe with reference beam data.The iSVS method may then extract the sample speckle field data from atleast one of the off-axis lobes and determine sample dynamic fromstatistics calculated from the sample speckle field data.

Although the iSVS methods in some of the examples of this Section aredescribed as determining sample dynamics from a single off-axisinterferogram, it would be understood that the disclosure is not solimiting. In other implementations, the iSVS methods can determinesample dynamics for each off-axis interferogram of a plurality ofoff-axis interferograms captured at different exposure times or capturedduring a single exposure time. In one such implementation, an iSVSmethod may further include determining a change in sample dynamics. Forexample, an iSVS method may calculate the movement speed of an object inthe sample during different exposure times to determine the change ofmovement speed over time, e.g., to take a measurement of pressure or tomeasure the solidification or changes in a substance such as a gel dueto temperature.

FIG. 2 illustrates an example of a sequence of operations of an iSVSmethod used to recover a sample speckle field pattern from an off-axisinterferogram recorded during a single exposure time, according to oneembodiment. In FIG. 2 , the sequence of the operations is denoted bydirectional arrows through depicted images 210, 210, 230, 240, and 250.In this illustrated example, the sequence of operations includes a firstoperation of subtracting a reference frame from the off-axisinterferogram, depicted as image 210, to generate a reference-subtractedimage, depicted as image 210. The reference frame may be, for example, a2D image having a uniform intensity that is equal to the reference beamintensity. This operation can suppress noise from non-uniformities inthe reference beam which may additionally avoid noise within the rangeof spatial frequencies that contain the sample signal. In anotherembodiment, this first operation is omitted, for example, inimplementations where there is little to no noise.

The sequence of operations illustrated in FIG. 2 also includes Fouriertransforming (e.g., using 3D fast Fourier transform) thereference-subtracted image, depicted as image 220, to generate aFourier-transformed reference-subtracted image, depicted as image 230.The Fourier-transformed data, depicted as image 230, includes a firstoff-axis lobe 232 and a second off-axis lobe 234, and a third lobe 236.The three lobes 232, 234, 236 include data of the reference beam and thesample beam. The first off-axis lobe 232 and the second off-axis lobe234 contain the sample field data. The third lobe 236 contains thereference beam data. The illustrated sequence of operations alsoincludes extracting the sample field data from one of the off-axis lobes232, 234 and dividing by the amplitude of the reference beam to yieldsample amplitude only. In one case, the sample field data from one ofthe off-axis lobes 232, 234 is spatially cropped, shifted to the centerof the spatial frequency space to remove the phase ramp of the referencebeam in the spatial domain, and divided by the amplitude of thereference beam.

In certain implementations, the iSVS method includes a croppingoperation to extract a sample field data from at least one of theoff-axis lobes in a off-axis interferogram in the frequency domain. Theknown tilt angle of the reference beam and the size of the rectangularaperture mask are used to determine the correct area of the spatialfrequency domain to filter out. A spatial frequency filter based on thisdetermined area of the spatial frequency domain can be used to crop thedata.

The sequence of operations illustrated in FIG. 2 also includes inverseFourier transforming the extracted data back to the spatial domain,yielding an image of the complex amplitude and phase of the samplespeckle field. The magnitude of the sample speckle field is directlyrelated to the decorrelation time of the light contributing to it. Inone aspect, one or more additional operations may be included to performanalysis of different spatial locations using the data from the complexamplitude and phase of the sample speckle field. The complex amplitudeand phase of the sample speckle field includes data at different spatiallocations that can represent contributions from different areas and pathlength distributions and can be used to extract more information fromthe sample. For example, this can be used to map the blood flow atdifferent locations in the brain, indicating the activity of differentparts of the brain.

According to one aspect, an iSVS method determines a decorrelation timefrom the sample speckle field data in the spatial frequency domainand/or from the image of the sample speckle field pattern in the spacedomain. The magnitude of the sample speckle field pattern is directlyrelated to the decorrelation time of the light contributing to it. Inone implementation, the iSVS method determined the decorrelation time ofa given area of the sample speckle field pattern by calculating theaverage of the sample electric field magnitude within that area anddetermining the decorrelation time from the calculated sample electricfield magnitude within that area using e.g., a mapping of differentvalues of sample electric field magnitude corresponding to differentdecorrelation times. For example, the iSVS method may use a lookup tablewith mappings of different visibility factors F to differentdecorrelation times to determine the decorrelation time corresponding tothe calculated average magnitude in that area. These mappings can beinferred from Eqn. 12 where decorrelation time i is linked to fringevisibility. In one aspect, an iSVS method may calculate a decorrelationtime for each of multiple areas and/or calculate multiple decorrelationtimes during each exposure time for each of one or more areas.

FIG. 3 is a flowchart depicting operations of an iSVS method implementedby an iSVS system, according to certain implementations. One or moreprocessors of the iSVS system may execute instructions that cause theone or more processors to perform the operations of the iSVS method.Although the iSVS method is described with reference to recoveringsample speckle field data from one off-axis interferogram anddetermining sample dynamics from statistics of taken from the samplespeckle field data, it would be understood that the disclosure is not solimiting. In another aspect, the iSVS method may recover sample specklefield data from a plurality of off-axis interferograms respectively anddetermine sample dynamics from the sample field data determined fromeach off-axis interferogram by applying the same operations as describedwith respect to FIG. 3 . The iSVS method may also include receiving theoff-axis interferogram from the camera or receiving or retrieving theoff-axis interferogram from memory, according to one implementation. Incertain implementations, the off-axis interferogram is a two-dimensionalimage captured by, e.g., a two-dimensional light detector array of acamera of an iSVS system. An example of a suitable two-dimensional lightdetector array is a CCD array. The iSVS method may also include sendingcontrol signals to the camera to activate recording of one or moreoff-axis interferograms.

At operation 320, sample speckle field data is recovered from anoff-axis interferogram recorded during a single exposure time. Forexample, the iSVS method may recover the sample speckle field data byFourier transforming the off-axis interferogram to generate data withoff-axis lobes containing the sample speckle field data and extractingat least one of the off-axis lobes from the spatial frequency space.Optionally, the sample speckle field pattern may be reconstructed byinverse Fourier transforming the extracted sample speckle field data.

At operation 340, sample dynamics are determined from specklesstatistics calculated from the sample speckle field data or from thesample speckle pattern recovered. An example of a speckle statisticsincludes an average or mean magnitude within a given area of the samplespeckle pattern. The area may be a portion of the sample speckle patternaccording to one aspect, or may be the entire sample speckle patternaccording to another aspect. Other examples of speckle statisticsinclude the standard deviation or additional moments of thedistribution. An example of sample dynamics is a decorrelation time ofthe sample speckle pattern or one or more areas of the sample specklepattern. Another example of sample dynamics is movement speed of one ormore objects in the sample. In one aspect, movement speed may becalculated from the calculated decorrelation time. In one aspect, thesample dynamics determined at operation 340 include one or more of adecorrelation time, a movement of one or more object in a sample, thechanges in the sample due to temperature, or the changes in a sample dueto solidification or phase change.

In one aspect, operation 340 includes calculating speckle statisticsfrom the sample speckle field data or the sample speckle pattern anddetermining the sample dynamics using the speckle statistics and/orother data. For example, operation 340 may calculate the average or meanmagnitude of a given area of the sample speckle pattern reconstructedand determine a correlation speed from the average or mean magnitude ofthe values of the sample speckle pattern in the given area. In one case,operation 340 may also calculate the movement of one or more objects inthe sample based on the correlation speed determined. According to oneaspect, the iSVS method uses a calibrated mapping between the sampledynamics and the speckle statistics and/or other data to determine thesample dynamics.

FIG. 4 is a flowchart depicting an example of sub-operations that may beincluded in operation 320 of FIG. 3 , according to certain aspects.Sub-operations depicted by dotted line boxes are optional.

At optional (denoted by the dotted line) sub-operation 422, the iSVSmethod subtracts a reference frame from the off-axis interferogram.Subtracting the reference frame from the off-axis interferogram maysuppress noise from non-uniformities in the reference beam. Thereference frame is an interferogram where the sample beam has beenblocked. Therefore, only the reference beam is illuminating the sensorand any non-uniformities can be captured.

At sub-operation 424, the iSVS method performs Fourier transformation(e.g. using fast Fourier transform) on the off-axis interferogram togenerate data in the spatial frequency domain with off-axis lobescontaining sample speckle field data. The iSVS system includes avertical slit at the Fourier plane that sets the shape of the samplespectrum (e.g., a rectangular vertical slit sets a rectangular shape ofthe sample spectrum and a circular vertical slit sets a circular shapeof the sample spectrum). The raw off-axis interferogram captured by thecamera of the iSVS system includes both sample speckle field andreference beam data. The tilt angle of the reference beam can bedesigned, according to one aspect, to position the off-axis lobescontaining sample speckle field data to the sides of the spatialfrequency spectrum without overlapping with other terms.

At sub-operation 425, the iSVS method extracts sample speckle field datafrom the at least one of the off-axis lobes in the spatial frequencydomain. In one implementation, the iSVS method extracts the samplespeckle field data by spatially cropping one of the off-axis lobes fromthe image, shifting the cropped data to the center of the spatialfrequency space, which can remove the phase ramp of the reference beamin the spatial domain, and then divide the data by the amplitude of thereference beam. In addition or alternatively, the iSVS method may selectone of the off-axis lobes. In other implementations, the data from theoff-axis lobe may be extracted by YoonSeok Baek, KyeoReh Lee, SeungwooShin, and YongKeun Park, “Kramers-Kronig holographic imaging forhigh-space-bandwidth product,” Optica 6, 45-51 (2019), which is herebyincorporated by reference in its entirety.

At sub-operation (denoted by dotted line) operation 426, the iSVS methodinverse Fourier transforms (e.g. using fast Fourier transform) the datato recover an image of complex amplitude and phase of the sample specklefield. The magnitude of the sample speckle field is directly related tothe decorrelation of the light contributed to it. With the image of thecomplex amplitude and phase of the sample speckle field, evaluation ofspeckle statistics and sample dynamics at different spatial locations ofthe sample can be performed. For example, in some implementations, theiSVS method may determine the decorrelation time for one or more areasof the sample and then determine the movement speed of an object orobjects in the one or more areas from the decorrelation times.

FIG. 5 is a flowchart depicting an example of sub-operations that may beincluded in operation 340 of FIG. 3 , according to certain aspects. Atsub-operation 542, the decorrelation time τ is determined. Thedecorrelation time τ can be determined from the sample speckle fielddata in the spatial frequency domain or from data taken from the imageof the complex amplitude and phase of the sample speckle field in thespace domain. In one implementation, the iSVS method determines thedecorrelation time τ for one or more spatial coordinates or areas of thesample using the image of the sample speckle field reconstructed, e.g.,from sub-operation 426. In this case, the iSVS method calculates theaverage of the sample electric field magnitude within each of the one ormore areas and then determines the decorrelation time from thecalculated sample electric field magnitude within those one or moreareas using e.g., a mapping of different values of sample electric fieldmagnitude corresponding to different decorrelation times. This mappingis described in Eqn. 12 by the relationship between the sampledecorrelation function g₁(t) and the fringe visibility. The magnitudemaps to the decorrelation time with smaller and larger field amplitudessignifying shorter and longer decorrelation times respectively.

At sub-operation 544, the iSVS method calculates a movement speed of anobject or objects in the sample based on the decorrelation time τdetermined from the sample speckle pattern. For example, the cerebralblood flow can be calculated using the decorrelation time τ. A method ofcalculating cerebral blood flow from decorrelation time τ can be foundin Selb, J., Boas, D. A., Chan, S. T., Evans, K. C. Buckley, E. M.,Carp, S. A., “Sensitivity of near-infrared spectroscopy and diffusecorrelation spectroscopy to brain hemodynamics: simulations andexperimental findings during hypercapnia,”Neurophotonics. 1, 15005(2014), which is hereby incorporated by reference in its entirety.

-   -   Calibration Method

Certain aspects pertain to methods for calibrating an iSVS system tocompare or map results (e.g., speckle statistics) from operating theiSVS system and/or performing an iSVS method to different values ofsample dynamics such as decorrelation times). FIG. 6 is a flowchartdepicting operations of an iSVS method for calibrating an iSVS system tomap effective visibility factors to different decorrelation times,according to an implementation.

At operation 620, a scattering sample (or samples) that is fluctuatingat a sequence of known decorrelation times or a calibration subsystemsimulating such as sample is introduced into an iSVS system. In oneexample, different driving voltages are applied sequentially to a motordriving a rotating diffuser to produce sample fluctuations at a sequenceof different correlation times where each driving voltage causes adifferent correlation time. The decorrelation times of the sample can bemeasured by another system such as a DCS system that measures the timetrace of the fluctuations using a single photon counting module.

FIG. 10A is a photograph of an example of components of a calibrationsubsystem of an iSVS system including a rotating diffuser 1010 and amotor and gearbox 1020, according to one aspect. The motor and gearbox1020 are in in electrical communication with the rotating diffuser 1010to apply one or more driving voltages. In response, the rotatingdiffuser 1010 rotates at a sequence of different speeds, which simulatessample fluctuations corresponding to a sequence of correlation times.

FIG. 10B is a schematic diagram of an example of components of acalibration subsystem of an iSVS system, according to one aspect. Inthis example, the calibration subsystem includes a first rotatingdiffuser 1025, a second static diffusor 1030, a beam splitter 1040, anda camera 1050. An example of diffusers that can be used are glassdiffusers such as the DG20 Series ground glass diffusers made byThorlabs. The first rotating diffuser 1025 has controlled rotatingspeeds and the second static diffusor 1030 is static. Duringcalibration, a laser beam illuminated the first rotating diffuser 1025and a range of rotation speeds was applied. The scattered light from thefirst rotating diffuser 1025 illuminated the second static diffuser 1030and was collected by an optical system. The second static diffuser 1030is used to eliminate the speckle pattern “smearing” effect that ispresent when using a single rotating diffuser. The decorrelation timeswere computed by measuring the time traces of the intensity fluctuationsusing a single photon counting module (SPCM) in the optical setup. Anexample of a commercially-available SPCM is the SPCM-AQRH-14 sold byPerkinElmer. By mapping rotation speed to the measured decorrelationtime, a dynamic sample can be simulated with known decorrelation times.

FIG. 11 is a graph with a plot of decorrelation times measured fordifferent motor speeds controlled by control signals from a motorcontroller in communication with the motor, according to animplementation. The graph includes mean and standard deviations for eachmotor speed.

Returning to FIG. 6 , at operation 640, a sequence of off-axisinterferograms are recorded by the iSVS system while the sample isfluctuating at the sequence of known decorrelation times respectively.Each of the off-axis interferograms in the sequence is recorded whilethe sample is fluctuating at one of the known decorrelation times. Atoperation 650, a sample speckle pattern is recovered from each off-axisinterferogram of the sequence of off-axis interferograms. Each samplespeckle pattern corresponds to a known decorrelation time. At operation660, speckle statistics are determined (e.g., visibility factorcalculated using Eqn. 12) of each sample speckle pattern. At operation680, a mapping of the speckle statistics (e.g., visibility factor) foreach of the known decorrelation times for the iSVS system is determined.

FIG. 12A is a graph of a plot of speckle contrast determined by an SVSsystem vs. decorrelation time. FIG. 12B is a graph of a plot ofeffective visibility factor determined by an iSVS system vs.decorrelation time. The iSVS system was calibrated using the calibrationiSVS method depicted by the flowchart shown in FIG. 6 . Comparing theerror bars on the iSVS curve in FIG. 12B to the SVS curve in FIG. 12A,the iSVS curve resulting from the iSVS method more accurately measuredchanges in decorrelation times.

IV. Interferometric Speckle Visibility Spectroscopy (iSVS) Systems

FIG. 7 is a simplified block diagram of components of an iSVS system 700in an off-axis holographic configuration, according to certainimplementations. The iSVS system 700 includes at least one laser 710 forprovided a laser beam and a first optical system 720 The first opticalsystem 720 is at least in part configured or configurable to split thelaser beam generated by the at least one laser 710 into a sample arm(also referred to herein as a “sample beam”) and a reference arm (alsoreferred to herein as a “reference beam”). The first optical system 720includes one or more optical components (e.g., one or more of a beamsplitter, a lens, an optical fiber, mirror, etc.). In one example, thefirst optical system 720 includes a beam splitter such as, e.g., apolarizing beam splitter that is configured to reflect a first componentof the laser beam with a particular polarization direction (e.g. 0degrees) while transmitting a second component of the laser beam with aperpendicular polarization direction (e.g. 90 degrees). An example of acommercially-available polarizing beam splitter is the polarizing beamsplitter PBS251 from Thorlabs.

The iSVS system 700 also includes a second optical system 730 that is atleast in part configured or configurable to collect light from thesample beam and relay the light to illuminate the sample 20 beingimaged. The second optical system 730 includes one or more opticalcomponents (e.g., one or more of a beam splitter, a lens, an opticalfiber, mirror, etc.). In one example, the second optical system 730includes a multimode fiber or a fiber bundle and the sample beam iscoupled into the multimode fiber or the fiber bundle and the output beamis collimated and is used to illuminate the sample, e.g., the foreheadof a human subject. An example of a suitable multimode fiber is the FB2,M31L02 made by Thorlabs.

During image acquisition, the sample 20 is illuminated by a sample beam.The illustrated example in FIG. 7 is shown at an instant in time duringan image acquisition operation of the iSVS system 700. At other times,the sample 20 need not be located at the iSVS system 700 and thus, thesample 20 is depicted as optional by the dotted line. According to oneaspect, the sample 20 is illuminated in reflection mode. According toanother aspect, the sample 20 is illuminated in transmission mode.

Returning to FIG. 7 , the iSVS system 700 also includes a third opticalsystem 740, a fourth optical system 750, one or more cameras 770 havingone or more sensors, and a computing system 780. The third opticalsystem 740 is at least in part configured or configurable to collect thesample beam and image the sample beam onto the one or more cameras 770.An example of a commercially-available camera that can be used is theS640 camera made by Phantom. The third optical system 740 includes oneor more optical components (e.g., one or more of a beam splitter, alens, an optical fiber, mirror, etc.). For example, the third opticalsystem 740 may include a multimode optical fiber or a fiber bundleconfigured to collect the diffused light from the sample. An example ofa multimode fiber that can be used is a large core multimode fiber suchas M107L02 multimode fiber (e.g., having a core diameter of about 1.5mm) made by Thorlabs. In this aspect, the multimode fiber is configuredto collect light from the sample 20 and relays the light onto the one ormore cameras 770. The third optical system 740 may also include, e.g., a4-f optical subsystem with two or more lenses. In another example, thethird optical system 740 may additionally or alternatively include avertical slit or other aperture located at the Fourier plane of the oneor more cameras 770. In this case, the sample beam is imaged onto thecamera after being spatially filtered by the aperture in the Fourierplane. The vertical slit or other aperture sets the shape of the samplespectrum in the frequency domain. In this example, the one or morecameras 770 are configured to record one or more interferograms that arelow-pass filtered images based on the size and shape of the aperture.The vertical slit can be circular, oval, rectangular, of othergeometrical shape. In implementations without a vertical slit or otheraperture located at the Fourier plane of the one or more cameras 770,the iSVS system 700 may use a technique such as described in WenjunZhou, Oybek Kholiqov, Shau Poh Chong, and Vivek J. Srinivasan, “Highlyparallel, interferometric diffusing wave spectroscopy for monitoringcerebral blood flow dynamics,” Optica 5, 518-527 (2018), which is herebyincorporated by reference in its entirety. In other words, thisexperimental setup is also suitable to measure the decorrelation in astandard DCS configuration by measuring the decorrelation time bysampling at high speed in time.

According to certain implementations, the iSVS system includes a laseror lasers. In one aspect, the iSVS system includes a laser that isoperable to provide laser light having wavelength between about 650 nmand 950 nm. The 650-950 nm optical window has relatively low opticalabsorption and therefore enables light to penetrate through the skin,scalp, and skull and interact with the brain. In one example, the laseris a 671-nm laser source that can provide a collimated 56 mW laser beamwith a 6-mm spot size that results in a <2 mW/mm2 irradiance for skinexposure within the American National Standard Institute (ANSI) limit.An example of a suitable commercially-available laser that can beimplemented is the CL671-15 laser sold by CrystaLaser® of Reno, Nev.When illuminating a skull, the returning photons from such illuminationmay carry information about the cerebral blood flow that can be used toinfer the brain activity via neurovascular coupling as discussed in Lou,H. C., Edvinsson, L., MacKenzie, E. T., “The concept of coupling bloodflow to brain function,”Ann. Neurol. 22, 289-297 (1987) and Dirnagl, U.,Niwa, K., Lindauer, U., Villringer, A., “Coupling of cerebral blood flowto neuronal activation: Role of adenosine and nitric oxide,” Am. J.Physiol.—Hear. Circ. Physiol. 267 (1994), which are hereby incorporatedby reference in their entireties.

Returning to FIG. 7 , the iSVS system 700 include one or more lasers 710that generate a laser beam, a first optical system 720 that splits thelaser beam into a reference beam and a sample beam, and a fourth opticalsystem 750. The fourth optical system 750 is at least in part configuredor configurable to collect light from the reference arm and generate anoff-axis reference beam incident on the one or more cameras 770 at anoblique angle θ (also referred to herein as the “tilt angle”). Thefourth optical system 750 includes one or more optical components (e.g.,one or more of a beam splitter, a lens, an optical fiber, mirror, etc.).In one aspect, the fourth optical system 750 includes an optical fiberfor spatial filtering such as a single mode fiber. An example of asingle mode fiber that can be used is a FB1, Thorlabs, PM460-HP made byThorlabs. In one aspect, the tilt angle is in a range of severaldegrees. The tilt angle is designed based on the maximum spatialfrequency bandwidth of the camera (determined by the pixel pitch) toensure that no aliasing occurs.

According to one aspect, fourth optical system 750 includes one or morecomponents configured to provide a tilt angle of the reference beam inorder to position the off-axis of the sample speckle pattern so that theoff-axis lobes containing sample data fit on the sides of the spatialfrequency spectrum without overlapping with the other portion. The angleis chosen along with the size of the aperture to ensure that theoff-axis lobes do not overlap with the sample autocorrelation term andalso do not cause any aliasing.

During an image acquisition operation of the iSVS system 700, anoff-axis reference beam interferes with scattered light from the sample20 at the one or more sensors of the camera(s) 710 and the camera(s)records one or more interferograms. In one aspect, one or moreinterferograms are recorded during one exposure time. In another aspect,one or more interferograms are recorded during one or more respectiveexposure times. The camera may include one or more image sensors. Someexamples of suitable image sensors are CMOS sensors, a charge-coupleddevice (CCD), and other similar devices. In one example, the samplingrate of the camera used is determined by the device properties, wheretypical sensors can have sampling rates up to ˜HMz level. In oneimplementation, camera is set to have an exposure time in the range ofabout one to three order of magnitude longer than the decorrelationtime. In typical blood flow measurement, the exposure time is set fromseveral milliseconds to hundreds of milliseconds. In anotherimplementation, depending on the dynamic properties of the measuredobject, the camera is set to have an exposure time in the range of aboutmicrosecond to about several seconds, depending on the common devicespecifications. Each interferogram is recorded during an exposure time.

Returning to FIG. 7 , the iSVS system 700 includes a computing system780 having one or more processors or other circuitry 782 and an internalnon-transitory computer readable media (CRM) 784 in electricalcommunication with the processor(s) or other circuitry 782. The imagedata output from the one or more cameras 770 is transmitted (or “sent”or “communicated”) in a signal to one or more processors or othercircuitry 782 of the computing system 780. The computing system 780 isin electrical communication with the one or more cameras 770 to sendcontrol signals for controlling operations of the one or more cameras770 and/or to receive one or more signals with image data such as one ormore interferograms. The computing system 780 is optionally (denoted bydotted line) in electrical communication with the at least one laser 710to send one or more control signals for controlling operations. Thecomputing system 780 includes one or more processors or other circuitry782 and an internal non-transitory computer readable medium 784 (e.g.,memory) in electrical communication with the one or more processors 782.

The processor(s) or other circuitry of the computing system of the iSVSsystem 700 and, additionally or alternatively, other externalprocessor(s) (e.g., a processor of the external computing system 789)can execute instructions stored on non-transitory computer readablemedia (e.g., internal non-transitory CRM 784 or optional external memory792) to perform operations of the iSVS system 700. For example, theprocessor(s) or other circuitry may execute instructions to performoperations of an iSVS method to process the interferograms to determinea decorrelation time of the sample being imaged and/or determine amovement speed of an object in the sample. As another example, theprocessor(s) or other circuitry may send control signals to activate thelaser(s) 710 and/or may send control signals to activate the camera(s)770 to record during one or more exposure times to record one or moreinterferograms during image acquisition.

According to certain implementations, the computing system of an iSVSsystem can perform parallel image processing. To perform parallel imageprocessing, the computing device generally includes at least oneprocessor (or “processing unit”). Examples of processors include, forexample, one or more of a general purpose processor (CPU), anapplication-specific integrated circuit, an programmable logic device(PLD) such as a field-programmable gate array (FPGA), or aSystem-on-Chip (SoC) that includes one or more of a CPU,application-specific integrated circuit, PLD as well as a memory andvarious interfaces.

The computing system of an iSVS system may be in communication withinternal memory device and/or an external memory device. The internalmemory device can include a non-volatile memory array for storingprocessor-executable code (or “instructions”) that is retrieved by oneor more processors to perform various functions or operations describedherein for carrying out various logic or other operations on the imagedata. The internal memory device also can store raw image data,processed image data, and/or other data. In some implementations, theinternal memory device or a separate memory device can additionally oralternatively include a volatile memory array for temporarily storingcode to be executed as well as image data to be processed, stored, ordisplayed. In some implementations, the computing system itself caninclude volatile and in some instances also non-volatile memory.

Returning to FIG. 7 , optionally (denoted by dotted lines) the iSVSsystem 700 includes a communication interface 785 and a display 786 incommunication with the communication interface 785. The computing system780 may be configured or configurable to output raw data, processed datasuch as image data, and/or other data over the communication interface785 for display on the display 786. Optionally (denoted by dashedlines), the iSVS system 800 may further include one or more of acommunication interface 787 and an external computing system 789 incommunication with the communication interface 787, a communicationinterface 790 and an external memory device 792 in communication withthe communication interface 790 for optional storage of data to theexternal memory device 792, and/or a communication interface 793 incommunication with a user interface 794 for receiving input from anoperator of the iSVS system 800. The optional user interface 794 is inelectrical communication with the iSVS system 800 through thecommunication interface 793 to be able to send a control signal to thecomputing system 780 based on input received at the user interface 794.

In some implementations, the iSVS system includes a computing systemconfigured or configurable (e.g., by a user) to: (i) output raw data,processed data such as image data, and/or other data over acommunication interface to a display, (ii) output raw image data as wellas processed image data and other processed data over a communicationinterface to an external computing device or system, (iii) output rawimage data as well as processed image data and other data over acommunication interface for storage in an external memory device orsystem, and/or (iv) output raw image data as well as processed imagedata over a network communication interface for communication over anexternal network (for example, a wired or wireless network). Indeed insome implementations, one or more of operations of an iSVS method can beperformed by an external computing device. The computing system may alsoinclude a network communication interface that can be used to receiveinformation such as software or firmware updates or other data fordownload by the computing device. In some implementations, an iSVSsystem further includes one or more other interfaces such as, forexample, various Universal Serial Bus (USB) interfaces or othercommunication interfaces. Such additional interfaces can be used, forexample, to connect various peripherals and input/output (I/O) devicessuch as a wired keyboard or mouse or to connect a dongle for use inwirelessly connecting various wireless-enabled peripherals. Suchadditional interfaces also can include serial interfaces such as, forexample, an interface to connect to a ribbon cable. It should also beappreciated that one or more of components of the iSVS system can beelectrically coupled to communicate with the computing device over oneor more of a variety of suitable interfaces and cables such as, forexample, USB interfaces and cables, ribbon cables, Ethernet cables,among other suitable interfaces and cables.

The described electrical communication between components of iSVSsystems may be able to provide power and/or communicate data. Theelectrical communication between components of the iSVS systemsdescribed herein may be in wired form and/or wireless form.

FIG. 8A is a schematic diagram of components of an iSVS system 800,according to one implementation. The iSVS system 800 is in an off-axisholographic configuration. The illustrated example is shown at aninstant in time during an image acquisition while the sample 22 is beingilluminated and imaged in reflection mode. During other operations, thesample 22 may not be present. The iSVS system 800 includes a laser 810(e.g., a 532 nm, diode-pumped solid-state, long coherence length, laser)configured to provide a laser beam and a first optical system includinga first beam splitter 820 configured to split the laser beam into asample arm (also referred to herein as a “sample beam”) and a referencearm (also referred to herein as a “reference beam”). In one example, thefirst beam splitter 820 is a polarizing beam splitter that is configuredto reflect a first component of the laser beam with a particularpolarization direction (e.g. 0 degrees) while transmitting a secondcomponent of the laser beam with a perpendicular polarization direction(e.g. 90 degrees). A half-wave plate 832 (Thorlabs WPH05M-532) is usedto rotate the polarization of the deflected beam to match thepolarization of the transmitted beam. An example of acommercially-available polarizing beam splitter is the polarizing beamsplitter PBS251 from Thorlabs.

The iSVS system 800 also includes a second optical system that is atleast in part configured or configurable collect and relay light fromthe sample beam to the sample 22 to illuminate the sample 22 beingimaged. The second optical system includes a neutral-density filter 832(Thorlabs NE10B) configured to filter light from the sample arm, amirror 834 (Thorlabs PF10-03-G01) configured to reflect light, a firstFP 836 (Thorlabs PAF2-A4A) configured to couple the light into the fiber838 (Thorlabs P1-460B-FC-5), and a single mode fiber 838 (ThorlabsP1-460B-FC-5) coupled to the sample arm to direct the sample beam to thesample 22 to illuminate it. The neutral-density filters enable controlof the laser intensity and the single mode fiber provides spatialfiltering of the sample beam and enables it to be flexibly routed to thesample.

The iSVS system 800 also includes a third optical system that is atleast in part configured or configurable to collect scattered light fromthe sample and image onto the camera 870 with a 4-f imaging system. Thethird optical system includes a first collection lens 841, an aperture842 (e.g., a vertical slit) at the Fourier plane of the camera 870 tospatially filter the sample beam, a second beam splitter 844, apolarizer 845, a second lens 846, and a third beam splitter 848 (e.g., aplate beam splitter). The first lens 841 (e.g., a lens having a focallength of 60 mm) and the second lens 846 (e.g., a lens having a focallength of 200 mm) are in a 4-f optical configuration. The collectionlens 841 is configured to collect light scattered by the sample 22 whilebeing illuminated. The polarizer 845 is configured to filter scatteredsample light out that does not share the same polarization as thereference beam. The third beam splitter 848 is configured to pass thescattered sample light and/or block light of other wavelength. The thirdoptical system is configured to collect scattered light from the sampleand image onto the camera 870 after being spatially filtered by theaperture 842 of the 4-f optical configuration.

The iSVS system 800 also includes a fourth optical system that is atleast in part configured or configurable to collect light from thereference arm and generate an off-axis reference beam incident on thecamera 870 at a tilt angle θ. An example of a commercially-availablecamera that can be used is the S640 camera made by Phantom. The fourthoptical system includes a second FP 852 configured to couple light tothe optical fiber, an optical fiber 853 coupled to the reference arm, adiffuser 854 configured to diffuse the light, a collimating lens 856configured to collimate the reference arm to generate a collimated planewave beam, and a mirror 858 configured to reflect the collimated beam tothe third beam splitter 848. In one example, the optical fiber 853 is asingle mode optical fiber for spatial filtering. An example of acommercially-available single mode fiber that can be used is a FB1,Thorlabs, PM460-HP made by Thorlabs. The third beam splitter reflectsthe collimated reference beam at a tilt angle θ to the camera 870. Thetilt angle θ is with respect to a normal axis at the plane of the camera870. The scattered light from the sample 22 is interfered with by thecollimated, tilted reference beam on the camera 870. In one aspect, thetilt angle is in a range of about 0 rad to about 0.1 rad. In anotheraspect, the tilt angle is in a range of about 0 degree to about 5.7degrees.

The iSVS system 800 also includes a computing system 880 having one ormore processors or other circuitry 882 and an internal non-transitorycomputer readable media (CRM) 884 in electrical communication with theprocessor(s) or other circuitry 882.

The processor(s) or other circuitry 882, additionally or alternatively,other external processor(s), can execute instructions stored on memorysuch as internal non-transitory CRM 884 to perform operations of theiSVS system 800. For example, the processor(s) or other circuitry 882may execute instructions to perform operations of an iSVS method toprocess the interferograms to determine a decorrelation time of thesample being imaged and/or determine a movement speed of an object inthe sample. In addition or alternatively, the processor(s) or othercircuitry may send control signals to activate the laser(s) 810 and/ormay send control signals to activate the camera(s) 870 to record duringone or more exposure times to record one or more interferograms duringimage acquisition.

The iSVS system 800 also includes a single photon counting module 862and a single mode fiber 864 coupled to the single photon counting module862. The single photon counting module 862 may be implemented to captureconventional DCS measurements of the sample dynamics for calibration ofthe iSVS system 800. The single photon counting module 862 and singlemode fiber 864 may be removed when calibration is not in process.

FIG. 8B is a schematic diagram of components of an iSVS system 900,according to certain implementations. The iSVS system 900 is in anoff-axis holographic configuration. The illustrated example is shown atan instant in time during an image acquisition while the sample 24 isbeing illuminated and imaged in transmission mode. During otheroperations, the sample 24 may not be present. The iSVS system 900includes a laser 910 (e.g., a 532 nm, diode-pumped solid-state, longcoherence length, laser) configured to provide a laser beam and a firstoptical system including a first beam splitter 920 configured to splitthe laser beam into a sample arm (also referred to herein as a “samplebeam”) and a reference arm (also referred to herein as a “referencebeam”). In one example, the first beam splitter 920 is a polarizing beamsplitter that is configured to reflect a first component of the laserbeam with a particular polarization direction (e.g., 0 degrees) whiletransmitting a second component of the laser beam with a perpendicularpolarization direction (e.g., 90 degrees). An example of acommercially-available polarizing beam splitter is the polarizing beamsplitter PBS251 from Thorlabs. A half-wave plate 832 (ThorlabsWPH05M-532) is used to rotate the polarization of the deflected beam tomatch the polarization of the transmitted beam.

The iSVS system 900 also includes a second optical system that is atleast in part configured or configurable collect and relay light fromthe sample beam to the sample 24 to illuminate the sample 24 beingimaged. The second optical system includes a neutral-density filter 832(Thorlabs NE10B) configured to filter light from the sample arm, amirror 834 (Thorlabs PF10-03-G01) configured to reflect light, a firstFP 836 (Thorlabs PAF2-A4A) configured to couple light into the fiber,and a single mode fiber 838 (Thorlabs P1-460B-FC-5) coupled to thesample arm to direct the sample beam to the sample 24 to illuminate it.

The iSVS system 900 also includes a third optical system that is atleast in part configured or configurable to collect scattered light fromthe sample in through transmission and image onto the camera 970 with a4-f imaging system. The third optical system includes a first collectionlens 941, an aperture 942 (e.g., a vertical slit) at the Fourier planeof the camera 970 to spatially filter the sample beam, a second beamsplitter 944, a polarizer 945, a second lens 946, and a third beamsplitter 948 (e.g., a plate beam splitter). The first lens 941 (e.g., alens having a focal length of 60 mm) and the second lens 946 (e.g., alens having a focal length of 200 mm) are in a 4-f opticalconfiguration. The collection lens 941 is configured to collect lightscattered by the sample 24 while being illuminated. The polarizer 945 isconfigured to filter scattered sample light out that does not share thesame polarization as the reference beam. The third beam splitter 948 isconfigured to pass the scattered sample light and/or block light ofother wavelength. The third optical system is configured to collectscattered light from the sample and image onto the camera 970 afterbeing spatially filtered by the aperture 942 of the 4-f opticalconfiguration.

The iSVS system 900 also includes a fourth optical system that is atleast in part configured or configurable to collect light from thereference arm and generate an off-axis reference beam incident on thecamera 970 at a tilt angle θ. An example of a commercially-availablecamera that can be used is the S640 camera made by Phantom. The fourthoptical system includes a second FP 952 (Thorlabs PAF2-A4A) configuredto couple light to the optical fiber, an optical fiber 953 (ThorlabsP1-460B-FC-5) coupled to the reference arm, a diffuser 954 (ThorlabsDG05-1500) configured to diffuse the light, a collimating lens 956(Thorlabs, LA1024) configured to collimate the reference arm to generatea collimated plane wave reference beam, and a mirror 958 (ThorlabsPF10-03-G01) configured to reflect the collimated beam to the third beamsplitter 948 (Thorlabs BSW25). In one example, the optical fiber 953(Thorlabs P1-460B-FC-5) is a single mode optical fiber for spatialfiltering. An example of a commercially-available single mode fiber thatcan be used is a FB1, Thorlabs, PM460-HP made by Thorlabs. The thirdbeam splitter reflects the collimated reference beam at a tilt angle 0to the camera 970 (Phantom S640). The tilt angle 0 is with respect to anormal axis at the plane of the camera 970 (Phantom S640). The scatteredlight from the sample 24 is interfered with by the collimated, tiltedreference beam on the camera 970 (Phantom S640). In one aspect, the tiltangle is in a range of about 0 rad to about 0.1 rad. In another aspect,the tilt angle is in a range of about 0 degree to about 5.7 degrees.

The iSVS system 900 also includes a computing system 980 having one ormore processors or other circuitry 982 and an internal non-transitorycomputer readable media (CRM) 984 in electrical communication with theprocessor(s) or other circuitry 982. The processor(s) or other circuitry982, additionally or alternatively, other external processor(s), canexecute instructions stored on memory such as internal non-transitoryCRM 984 to perform operations of the iSVS system 900. For example, theprocessor(s) or other circuitry 982 may execute instructions to performoperations of an iSVS method to process the interferograms to determinea decorrelation time of the sample being imaged and/or determine amovement speed of an object in the sample. In addition or alternatively,the processor(s) or other circuitry may send control signals to activatethe laser(s) 910 and/or may send control signals to activate thecamera(s) 970 to record during one or more exposure times to record oneor more interferograms during image acquisition.

The iSVS system 900 also includes a single photon counting module 962and a single mode fiber 964 coupled to the single photon counting module962. The single photon counting module 962 may be implemented to captureconventional DCS measurements of the sample dynamics for calibration ofthe iSVS system 900. The single photon counting module 962 and singlemode fiber 964 may be removed when calibration is not in process.

Examples of Aperture Configurations

In certain implementations described herein, the iSVS system includes anaperture (e.g., vertical slit) at the Fourier plane of its camera. Thecamera is configured to record one or more interferograms that arelow-pass filtered images based on the size and shape of the aperture.Some examples of shapes of aperture that are used in variousimplementations include circular, oval, rectangular, of othergeometrical shape. The aperture sets the shape of the sample spectrum inthe spatial frequency domain. In one aspect, the aperture is designed toincrease or maximize the spatial bandwidth of the collected samplesignal.

The available bandwidth in the spatial frequency domain for off-axisholography can be expressed by the four terms in Eqn. 2. In the spatialfrequency domain, these four terms form the following signals: (i) thesample autocorrelation which is a convolution of the sample with itselfand therefore has a bandwidth of 2 B where B is the signal bandwidth,(ii) the reference autocorrelation which is a sharply peaked delta-likefunction, and (iii) the two off-axis lobe terms which are theconvolution of the sample with a shifted delta function from the tiltedreference beam. To increase or maximize the bandwidth of the samplesignal in the spatial frequency domain, an aperture may be selected todesign the shape and size of the sample bandwidth such that the off-axislobes may maximally or have an increased fit in the spatial frequencydomain without the off-axis lobes with the sample autocorrelation termor aliasing.

In iSVS systems, the sample field is a speckle field and increasing ormaximizing the number of speckles sampled is desired. A circular pupilleaves unused space in the spatial frequency domain around the circularpupil. To increase or maximize the number of speckle grains that aresampled, the iSVS systems, of certain implementations, are designed tohave the speckle field cover an increased or maximum number of imagingpixels at the camera and to increase or maximize the spatial frequencybandwidth (smallest speckle size) allowable without aliasing. Forexample, in one aspect, an iSVS system implements a rectangular aperturein the Fourier plane to set the shape of the sample spectrum to increasethe space in the spatial frequency domain. This iSVS system can then usethe tilt angle of the reference beam to position the off-axis lobes sothat they fit on the sides of the spatial frequency spectrum withoutoverlapping with the other terms.

FIG. 9A is an illustration of an example of an off-axis holographyspatial frequency spectrum with a circular sample bandwidth implementedby using a circular aperture at the Fourier plane, according to animplementation. Using the circular aperture enables maintainingisotropic lateral resolution but may not efficiently use the informationcapacity of the system since there is unused space (shown shaded ingray) in the spatial frequency domain. The off-axis holography spatialfrequency spectrum includes two off-axis lobes, each with a bandwidth ofB and a central third lobe having a bandwidth of 2 B where B is thesample signal bandwidth.

FIG. 9B is an illustration of an example of an off-axis holographyspatial frequency spectrum with a rectangular sample bandwidthimplemented by using a rectangular aperture at the Fourier plane,according to an implementation. By using the rectangular aperture toshape limit the spatial frequency content of the sample field, thespatial frequency domain can be fully used. The off-axis holographyspatial frequency spectrum includes two off-axis lobes, each with abandwidth of B and a central third lobe having a bandwidth of 2 B whereB is the sample signal bandwidth.

V. Examples of Results

-   -   Decorrelation Caused by Breathing and Blood Flow in Rodents

An iSVS system such as, e.g., the iSVS system 800 described with respectto FIG. 8 , was used to measure the dynamic decorrelation caused bybreathing and blood flow in a rat. The iSVS system was first calibratedusing an iSVS calibration method such as the method described withrespect to the flowchart shown in FIG. 6 . During image acquisition, theiSVS system was used to illuminate the dorsal skin flap of theanesthetized rat in both transmission and reflection modes and a seriesof frames of off-axis interferograms were recorded by the camera. TheiSVS system implemented an iSVS method such as, e.g., the method shownin FIG. 3 , to process the series of off-axis interferograms to analyzethe dynamic behavior of the captured light. For comparison, an SVSsystem was also used to image the dorsal skin flap of the anesthetizedrat in both transmission and reflection modes.

FIGS. 13A, 14A, 15A, 16A, 17A, and 18A are graphs with plots ofeffective speckle visibility over time (seconds) for the dorsal skinflap as measured by the iSVS system in transmission mode (e.g., iSVSsystem 900 shown in FIG. 8B) where the laser powers were 1 mW, 0.5 mW,0.26 mW, 0.13 mW, 0.06 mW, and 0.03 mW respectively, according toimplementations. During operation, the camera of the iSVS systemrecorded a series of interferograms while the sample beam power wasreduced in steps from 1 mW, 0.5 mW, 0.26 mW, 0.13 mW, 0.06 mW, and 0.03mW.

FIGS. 13B, 14B, 15B, 16B, 17B, and 18B are graphs with plots of specklecontrast over time (seconds) for the dorsal skin flap as measured by anSVS system in transmission mode for comparison where the laser powerswere 11 mW, 0.5 mW, 0.26 mW, 0.13 mW, 0.06 mW, and 0.03 mW respectively,according to implementations. During operation, the camera of the SVSsystem recorded a series of images while the sample beam power wasreduced in steps from 1 mW, 0.5 mW, 0.26 mW, 0.13 mW, 0.06 mW, and 0.03mW.

FIGS. 19A, 20A, 21A, 22A, 23A, and 24A are graphs with plots ofeffective speckle visibility over time (seconds) for the dorsal skinflap as measured by the iSVS system in reflection mode (e.g., iSVSsystem 800 shown in FIG. 8A) where the laser powers were 1 mW, 0.5 mW,0.26 mW, 0.13 mW, 0.06 mW, and 0.03 mW respectively, according toimplementations. During operation, the camera of the iSVS systemrecorded a series of interferograms while the sample beam power wasreduced in steps from 1 mW, 0.5 mW, 0.26 mW, 0.13 mW, 0.06 mW, and 0.03mW.

FIGS. 19B, 20B, 21B, 22B, 23B, and 24B are graphs with plots of specklecontrast over time (seconds) for the dorsal skin flap as measured by anSVS system in reflection mode for comparison where the laser powers were1 mW, 0.5 mW, 0.26 mW, 0.13 mW, 0.06 mW, and 0.03 mW respectively,according to implementations. During operation, the camera of the SVSsystem recorded a series of images while the sample beam power wasreduced in steps from 1 mW, 0.5 mW, 0.26 mW, 0.13 mW, 0.06 mW, and 0.03mW.

As can be seen in, for example, FIG. 17B, FIG. 18B, FIG. 23B, and FIG.24B, when the signal light intensity drops to lower levels with laserpower set at lower levels, the decorrelation signal with specklecontrast from the SVS system appears to be buried in camera noise, andthe SVS system can no longer accurately detect decorrelation signalchanges. Due to the heterodyne gain provided by the reference beam inthe iSVS system, the iSVS system can detect the decorrelation signal dueto breathing and even the blood flow from heat beating down to a samplelaser beam power of 0.06 mW as shown in FIG. 17A for transmission modeand as shown in FIG. 23A for reflection mode. The iSVS system detected adecorrelation signal due to breathing that has a frequency of about ⅔ Hzand a decorrelation signal due blood flow from heart beating that has afrequency of about 6 Hz. These frequencies are determined by analyzingthe Fourier transform of the measured time traces and isolating thelocations of peaks in the frequency spectrum.

-   -   In Vivo Measurement of Cerebral Blood Flow in Humans

FIG. 25 is a schematic diagram of components of an iSVS system 2500,according to an embodiment. The iSVS system 2500 includes a first halfwave plate labeled “HWP1,” a plate beam splitter labeled “PBS,” a secondhalf wave plate labeled “HWP2,” a first signal labeled “S1,” a firstneutral-density filter labeled “ND1,” a first fiber coupler labeled“FC1″coupled to the first neutral-density filter ND1, a first fiberbundle labeled “FBI” coupled to the first fiber coupler FCI, a firstlens labeled “L1,” a first mirror labeled “M1,” and a second mirrorlabeled “M2,” a second signal labeled “S2,” a second neutral-densityfilter labeled “ND2,” a second fiber coupler labeled “FC2” coupled tothe second neutral-density filter ND2, a second fiber bundle labeled“FB2” coupled to the second fiber coupler FC2, a third fiber couplerlabeled “FC3” coupled to the FB2, a third fiber bundle labeled “FB3”receiving scattered light from the human subject 26, a second lenslabeled “L2,” an aperture labeled “AP” at the Fourier plane of thecamera, a polarizer labeled “P,” a third lens labeled “L3,” a first beamsplitter labeled “BS1,” a second beam splitter labeled BS2,” and acamera labeled “CAM.” The iSVS system 2500 is shown during an imageacquisition operation while a human subject 26 is being imaged. A singlephoton counting module (SPCM) is also included. The second beam splitteris included to split the light onto the single-photon-counting modulefor a calibration operation. Non-contact source and detector fiberscoupled to the third fiber coupler FC3 were mounted above the humansubject forehead over the prefrontal cortex area. The iSVS system 2500also includes a laser configured to generate an illuminating laser beamsuch as a laser beam from a 671-nm laser source. In this example, thesecond fiber bundle FB2 is a multimode fiber such as, e.g., thecommercially-available M31L02 multimode fiber sold by Thorlabs with˜3000 modes. The laser beam was coupled to the second fiber bundle FB2.In one example, a collimated 56 mW laser beam with a 6-mm spot sizeresulted in a <2 mW/mm² irradiance for skin exposure. The diffused lightat various source-detector separations was collected by the third fiberbundle FB3. In one example, the third fiber bundle FB3 is a large coremultimode fiber such as the commercially-available M107L02 large coremultimode fiber sold by M107L02 with a core diameter of 1.5 mm andcontaining ˜6 million modes. The output from the third fiber bundle FB3was channeled through the sample arm of the interferometric setup wherethe diffused light and the reference beam are combined by the beamsplitter and recorded by the camera.

The iSVS system 2500 was implemented to monitor the blood flow in humanswhen the reflected light signal was low. When the S-D separation was 1.5cm, the photon count rate read by the SPCM was ˜1500 counts/second,while the dark count rate of the SPCM was ˜180 counts/second. The iSVSsystem 2500 took measurements used to generate the intensitydecorrelation curve g2(t) shown in FIG. 26 based on a measurement timeof 50 s. FIG. 26 is a graph of a plot of the intensity decorrelationcurve g2(t) measured by the iSVS system 2500, according to an example.The decorrelation time is ˜50 μs.

The ISVS system with a camera exposure time of 2 ms and an FPS of 100 Hzyielded a pulsatile signal trace, shown by the dotted line in FIG. 27 .The filtered signal trace is the solid line in FIG. 27 .

The visibility factor measured by the ISVS system 2500 was used tocalculate the blood flow index (BFI) based on the tissue scatteringparameters used in Durduran, T., Choe, R., Baker, W. B., Yodh, A. G.,“Diffuse optics for tissue monitoring and tomography,” Reports Prog.Phys. 73 (2010), p. 76701, which is hereby incorporated by reference inits entirety. The raw and filtered BFI traces are presented in blue andred curves in FIG. 28 , respectively. The Fourier transform of the rawBFI trace is shown in FIG. 29 , and the heart-beat frequency ˜1.1 Hz andits harmonics are highlighted. In this experimental configuration, theaverage photon electron number of the signal beam on each camera pixelwas ˜0.95, where the detector noise was ˜1.2 photon electrons. In thiscase, the SNR for each pixel was ˜0.79.

The iSVS system 2500 was used to take measurements for three cases: (i)An S-D separation of d₁=1.5 cm while the human subject 26 went through abreath-holding task, (ii) an S-D separation of d₁=0.75 cm while thehuman subject 26 went through a breath-holding task, and (iii) an S-Dseparation of d₂=1.5 cm while the human subject 26 breathed normally.The representative recorded traces for case (i), (ii) and (iii) areshown in FIG. 30 and FIG. 31 , respectively. For each case, fiverepetitive experiments were conducted.

To see the rCBF change due to the breath holding task, the mean valuesand standard deviations of rCBF during 2-4 s (Phase 1), 10-12 s (Phase2, first several seconds of breath holding), 22-24 s (Phase 3, lastseveral seconds of breath holding) and 37-39 s (Phase 4) were calculatedand plotted, as shown in FIG. 32 . The increase of rCBF values in Phase3 at the S-D separation of 15 mm (case (i)) is clearly shown by thesolid line in FIG. 32. In this case (S-D separation of 1.5 cm), some oflight interacted with the cerebral blood flow. Blood flow change couldbe seen at an S-D separation larger than 1 cm as can be found in Selb,J., Boas, D. A., Chan, S. T., Evans, K. C., Buckley, E. M., Carp, S. A.,“Sensitivity of near-infrared spectroscopy and diffuse correlationspectroscopy to brain hemodynamics: simulations and experimentalfindings during hypercapnia,”Neurophotonics. 1, 15005 488 (2014), whichis hereby incorporated by reference in its entirety. The increase ofrCBF values in Phase 3 at the S-D separation of 7.5 mm (case (iii)) wasnot as clear as that in case (i), as shown by the dotted line in FIG. 32. In this case (S-D separation of 0.75 cm), most of light interactedwith the forehead skin rather than the brain, hence the breath holdingtask did not have the same significant impacts on the signal. The normalbreathing measurements at the S-D separation of 1.5 cm (case (iii)) as areference did not have significant change of rCBF, as shown by thedashed line in FIG. 32 .

Modifications, additions, or omissions may be made to any of theabove-described embodiments without departing from the scope of thedisclosure. Any of the embodiments described above may include more,fewer, or other features without departing from the scope of thedisclosure. Additionally, the steps of described features may beperformed in any suitable order without departing from the scope of thedisclosure. Also, one or more features from any embodiment may becombined with one or more features of any other embodiment withoutdeparting from the scope of the disclosure. The components of anyembodiment may be integrated or separated according to particular needswithout departing from the scope of the disclosure.

It should be understood that certain aspects described above can beimplemented in the form of logic using computer software in a modular orintegrated manner. Based on the disclosure and teachings providedherein, a person of ordinary skill in the art will know and appreciateother ways and/or methods to implement the present invention usinghardware and a combination of hardware and software.

Any of the software components or functions described in thisapplication, may be implemented as software code using any suitablecomputer language and/or computational software such as, for example,Java, C, C#, C++ or Python, LabVIEW, Mathematica, or other suitablelanguage/computational software, including low level code, includingcode written for field programmable gate arrays, for example in VHDL.The code may include software libraries for functions like dataacquisition and control, motion control, image acquisition and display,etc. Some or all of the code may also run on a personal computer, singleboard computer, embedded controller, microcontroller, digital signalprocessor, field programmable gate array and/or any combination thereofor any similar computation device and/or logic device(s). The softwarecode may be stored as a series of instructions, or commands on a CRMsuch as a random access memory (RAM), a read only memory (ROM), amagnetic medium such as a hard-drive or a floppy disk, or an opticalmedium such as a CD-ROM, or solid stage storage such as a solid statehard drive or removable flash memory device or any suitable storagedevice. Any such CRM may reside on or within a single computationalapparatus, and may be present on or within different computationalapparatuses within a system or network. Although the foregoing disclosedembodiments have been described in some detail to facilitateunderstanding, the described embodiments are to be consideredillustrative and not limiting. It will be apparent to one of ordinaryskill in the art that certain changes and modifications can be practicedwithin the scope of the appended claims.

The terms “comprise,” “have” and “include” are open-ended linking verbs.Any forms or tenses of one or more of these verbs, such as “comprises,”“comprising,” “has,” “having,” “includes” and “including,” are alsoopen-ended. For example, any method that “comprises,” “has” or“includes” one or more steps is not limited to possessing only those oneor more steps and can also cover other unlisted steps. Similarly, anycomposition or device that “comprises,” “has” or “includes” one or morefeatures is not limited to possessing only those one or more featuresand can cover other unlisted features.

All methods described herein can be performed in any suitable orderunless otherwise indicated herein or otherwise clearly contradicted bycontext. The use of any and all examples, or exemplary language (e.g.“such as”) provided with respect to certain embodiments herein isintended merely to better illuminate the present disclosure and does notpose a limitation on the scope of the present disclosure otherwiseclaimed. No language in the specification should be construed asindicating any non-claimed element essential to the practice of thepresent disclosure.

Groupings of alternative elements or embodiments of the presentdisclosure disclosed herein are not to be construed as limitations. Eachgroup member can be referred to and claimed individually or in anycombination with other members of the group or other elements foundherein. One or more members of a group can be included in, or deletedfrom, a group for reasons of convenience or patentability. When any suchinclusion or deletion occurs, the specification is herein deemed tocontain the group as modified thus fulfilling the written description ofall Markush groups used in the appended claims.

What is claimed is:
 1. An interferometric speckle visibilityspectroscopy system, comprising: one or more optical systems configuredto interfere at least one off-axis reference beam with a sample signal;one or more sensors configured to record at least one off-axisinterferogram over an exposure time; and one or more processorsconfigured to execute instructions to: (i) recover speckle field data ora speckle field pattern based at least in part on the at least oneoff-axis interferogram; and (ii) determine at least one decorrelationtime based at least in part on speckle statistics of the speckle fielddata or the speckle field pattern.
 2. The interferometric specklevisibility spectroscopy system of claim 1, wherein the one or moreoptical systems includes a multimode fiber or a fiber bundle configuredto collect light from a sample being illuminated during operation. 3.The interferometric speckle visibility spectroscopy system of claim 2,wherein the sample is being illuminated during operation by at least onelaser beam.
 4. The interferometric speckle visibility spectroscopysystem of claim 2, wherein the one or more optical systems areconfigured to pass light collected by the multimode fiber or the fiberbundle to the one or more sensors.
 5. The interferometric specklevisibility spectroscopy system of claim 4, wherein the one or moresensors include one or more of a single photon counting device, anavalanche photodetector, a complementary metal-oxide-semiconductor(CMOS) sensor, a charge-coupled device (CCD), or a single photonavalanche diode.
 6. The interferometric speckle visibility spectroscopysystem of claim 1, wherein recovering the speckle field data comprises:(a) Fourier transforming the at least one off-axis interferogram togenerate data in spatial frequency space comprising at least oneoff-axis lobe; and (b) using a spatial frequency filter to crop thespeckle field data from the at least one off-axis lobe.
 7. Theinterferometric speckle visibility spectroscopy system of claim 6,wherein (a) comprises shifting the cropped speckle field data to acentral region in spatial frequency space.
 8. The interferometricspeckle visibility spectroscopy system of claim 6, wherein (a) comprisessubtracting a reference interferogram from the at least one off-axisinterferogram.
 9. The interferometric speckle visibility spectroscopysystem of claim 8, wherein the reference interferogram has a uniformintensity.
 10. The interferometric speckle visibility spectroscopysystem of claim 9, wherein: the at least one off-axis interferogramcomprise two off-axis interferograms recorded at different exposuretimes; and (b) comprises determining a change in sample dynamics in thetwo off-axis interferograms.
 11. The interferometric speckle visibilityspectroscopy system of claim 1, wherein the one or more processors areconfigured to determine sample dynamics from the speckle statistics ofthe speckle field data or the speckle field pattern.
 12. Theinterferometric speckle visibility spectroscopy system of claim 1,wherein the one or more processors are configured to determine amovement in a sample being analyzed from the at least one decorrelationtime.
 13. The interferometric speckle visibility spectroscopy system ofclaim 1, wherein the one or more processors are configured to monitorblood flow in a tissue sample based at least in part on the at least onedecorrelation time.
 14. The interferometric speckle visibilityspectroscopy system of claim 1, wherein the one or more processors areconfigured to calculate a blood flow index of a tissue sample based atleast in part on a visibility factor.
 15. The interferometric specklevisibility spectroscopy system of claim 1, wherein the exposure time isgreater than the at least one decorrelation time.